FR2996655A1 - Computer-implemented method for regrouping ordered initial list of elementary tasks, involves pre-selecting modified lists of elementary tasks satisfying predetermined criteria, and selecting final list from modified lists - Google Patents

Abstract

This computer-assisted method of reordering an ordered initial list of elementary tasks, to be executed using resources, into a final reordered list of elementary tasks, comprises the following steps: - grouping (20) the elementary tasks of the initial list in process, each process consisting of an ordered sub-list of elementary tasks, each elementary task belonging to a process, the processes being independent, - the grouping (24) of the elementary tasks into queues, each queue being associated with a respective resource and formed of an ordered sub-list of elementary tasks to be executed using this resource; - preselecting (28) a plurality of modified lists of elementary tasks satisfying a predetermined pre-selection criterion, by applying a first predetermined algorithm to the initial list, each modified list ee taking the basic tasks of the initial list in a different order, and - selecting (30) the final list from the lists modified by application of a second predetermined algorithm to all the modified lists.

Description

The present invention relates to the field of task scheduling and the sub-domain of plan management, that is, the phase of scheduling of tasks. control of the execution of a task list that was previously calculated. More particularly, the present invention relates to a computer-implemented method of reordering an ordered initial list of elementary tasks, to be executed using resources, into a final reordered list of elementary tasks. In general, such a method is implemented when the execution of the initial list of elementary tasks is interrupted following the occurrence of an unforeseen event, for example when a resource becomes inoperative or when it becomes unavailable. proves that an elementary task not yet performed may last longer than expected. Such a method then makes it possible to reschedule all the elementary tasks remaining to be executed, so as to obtain a new ordered list of elementary tasks. The total duration of the new list is then optimized with respect to the total duration of the initial list, recalculated after the occurrence of the event. It is possible to reschedule using the modeling used to calculate the initial list to calculate the new ordered list. While such methods generally make it possible to obtain a new ordered list of elementary tasks of minimized duration, they do not however make it possible to limit the differences between the initial list and the new list. As a result, the organization of the resources needed to perform the basic tasks is likely to be highly disturbed. This is unsatisfactory, especially from the point of view of the organization of any human resources involved in the conduct of the plan.

An object of the invention is therefore to propose a method of reordering an initial ordered list of elementary tasks into a final reordered list of tasks making it possible to limit the differences between the initial list and the final list, while ensuring a minimization of the duration of execution of the final list. For this purpose, the subject of the invention is a method, implemented by computer, of reordering an initial ordered list of elementary tasks, to be executed using resources, into a final reordered list of elementary tasks, the resources being non-shareable and being grouped into resource classes, each elementary task being executable by each resource of the same class, each elementary task being associated in the initial list with a resource, characterized in that it comprises the following steps: the grouping of the elementary tasks from the initial list into a process, each process being formed of an ordered sub-list of elementary tasks, each elementary task belonging to a process, the processes being independent, the grouping of the elementary tasks into files; wait, each queue being associated with a respective resource and formed of a sub-list ord elementary tasks to be performed using this resource, - preselecting a plurality of modified lists of elementary tasks satisfying a predetermined preselection criterion, by applying a first predetermined algorithm to the initial list, each modified list repeating the elementary tasks of the initial list in a different order, and - selecting the final list from the lists modified by application of a second predetermined algorithm to all the modified lists. Advantageously, the reordering method according to the invention takes into account potential uncertainties over the duration of the elementary tasks.

Advantageously, the reordering method according to the invention is independent of the modeling used for calculating the initial list of tasks and is thus robust to possible errors due to the modeling used. According to other advantageous aspects of the invention, the reordering method comprises one or more of the following characteristics, taken in isolation or in any technically possible combination: the first algorithm comprises: carrying out an elementary modification consisting of moving a target elementary task from a first queue of a first resource to a second queue of a second resource of the same class as the first resource, - the calculation of a parameter representative of the elementary modification, said representative parameter being calculated from a time interval representative of an uncertainty concerning the duration of execution, following said elementary modification, of at least one process, the iteration of the two preceding steps step by step, for each elementary task in each queue, and for each position of the elementary task in a second queue, - the preselection, according to the preselection criterion, of at least one elementary modification, - the determination of a modified list respectively for the or each preselected elementary modification, - the determination of a given datum. representative of the or each modified list, - the iteration of the previous six steps from each modified list determined at the previous iteration, until reaching a predefined maximum number of elementary modifications within a modified list with respect to the initial list; the step of determining a datum representative of the or each modified list consists of calculating the duration of execution of this modified list, the representative datum being the result of this calculation; the step of calculating a parameter representative of the elementary modification comprises the preliminary construction of fuzzy variables, each fuzzy variable being formed of a time interval representative of an uncertainty concerning the duration of execution, following said elementary modification , a complex task, the representative parameter being calculated from the fuzzy variables constructed; during the step of calculating a parameter representative of the elementary modification, the representative parameter is calculated from a risk aversion rate, the risk aversion rate being the level of preference attributed to the fact to obtain a guaranteed final list duration in relation to obtaining a potentially shorter, but unsecured, final list term; during the step of selecting the final list, the second algorithm comprises a step of determining at least one preselected list satisfying a first predetermined selection criterion, and a step of selecting the final list from the at least one pre-selected list; the second algorithm further comprises a step of testing the uniqueness of said at least one preselected list, the final list being taken as identical to said preselected list during the step of selecting the final list, if the test of uniqueness is positive; the method further comprises, if the uniqueness test is negative during the test step, a step of determining, among the plurality of preselected lists satisfying the first predetermined selection criterion, a preselected list satisfying a second one; predetermined selection criterion, the final list being taken as identical to said preselected list during the step of selecting the final list; in the step of determining a preselected list satisfying a second predetermined selection criterion, the second predetermined selection criterion consists in presenting the smallest distance to the initial list, the distance of a first list to a second list; being the square root of the sum of the squares of the temporal gaps between the instants of start of execution on the one hand, and the time differences between the instants of end of execution on the other hand, between the elementary tasks of the first and second lists that belong to the same process and are associated with different resources in the same resource class; the method comprises an initial compression step of the initial list of elementary tasks, the compression consisting in the maximum reduction of the execution time of said initial list being able to be obtained without modifying the order of execution of each elementary task by to each elementary task that conditions it in this list. The features and advantages of the invention will become apparent on reading the description which follows, given solely by way of nonlimiting example, and with reference to the appended drawings, in which: FIG. 1 is a diagram schematically illustrating a computer-assisted method of reordering an ordered initial list of elementary tasks, to be executed using resources, into a final reordered list of elementary tasks; FIG. 2 is a diagram schematically illustrating the process grouping of the elementary tasks of the initial list of FIG. 1, and the association of each elementary task with one of the resources; Fig. 3 is a flow chart showing steps of the reordering process illustrated in Fig. 1; FIG. 4 is a flowchart representing a step of preselecting a plurality of modified lists of elementary tasks of the method; and - Figure 5 is a flow chart showing a step of selecting the final list from the modified lists of the method. FIG. 1 schematically illustrates a method according to the invention, of reordering an initial list Li ordered of elementary tasks 10, to be executed using resources 12, into a final list Lf reordered of the elementary tasks 10. The list initial Li, respectively the final list Lf, is a list of elementary tasks executable at the initial date, respectively at the final date, of implementation of the method. The method according to the invention is implemented by a computer 13. In the exemplary embodiment, the initial list Li comprises a first elementary task 10a, a second elementary task 10b and a third elementary task 10c. The first elementary task 10a is located in the first position in the initial list Li, ie it is intended to be executed in first position in the initial list Li. The second elementary task 10b and the third elementary task 10c respectively are located in the second position. respectively in third position in the initial list Li. In addition, the second elementary task 10b is located at the first position in the final list Lf.

As illustrated in FIG. 2, each elementary task 10 belongs to a single process 14. Each process 14 is composed of one or more elementary tasks 10 necessary for its execution. Processes 14 are independent, i.e. they are executable independently of one another. In the exemplary embodiment, the first elementary task 10a of the initial list Li belongs to a first process 14a and the second elementary task 10b belongs to a second process 14b. The first process 14a further comprises the third elementary task 10c. In the example of a management plan for a crisis situation, for example a health crisis, each process consists for example in the evacuation of a victim and includes all the basic tasks necessary to this evacuation. Each elementary task 10 has a start time Ti, an end time Tf and a duration d. Each elementary task 10 also has prerequisites necessary for its execution.

Each resource 12 is a physical resource capable of enabling the execution of at least one elementary task 10. In the field of plan management, for example of a management plan of a health crisis situation, the resources 12 are, for example, emergency vehicles such as ambulances or vehicles for extricating victims. According to this same example, the initial list Li is the actual crisis management plan, that is to say the ordered set of elementary tasks necessary to implement to solve the crisis situation. Resources 12 are non-sharable and are grouped into resource classes 16. Each resource class 16 is a set of interchangeable resources. In the example of a management plan for a health crisis situation, a particular class of resources 12 consists for example of all the ambulance vehicles. Another class of resources is for example made up of all extrication vehicles. Each elementary task 10 is executable by a single resource 12 of a class 16 in the initial list Li. In the exemplary embodiment, the first elementary task 10a of the initial list Li is associated with a first resource 12a belonging to a class 16a of resources. Class 16a further comprises a second resource 12b. The first elementary task 10a of the initial list Li is executable by each of the resources 12a, 12b. The execution time D of an ordered list of elementary tasks 10 is defined as the time required to execute all the processes 14 associated with the list.

For example, the initial list Li, respectively the final list Lf, has a duration of execution Di, respectively Df. The distance Q of a first ordered list of elementary tasks 10 to a second ordered list of elementary tasks 10 is also defined as being the square root of the sum of the squares of the time differences between the start times of execution Ti of a on the other hand, and time differences between the times of completion Tf on the other hand, between the elementary tasks 10 of the first and second lists which belong to the same process 14 and are associated with resources of the same class 16 of resources 12.

The initial list Li ordered of elementary tasks 10 satisfies the following assumptions: i) the initial list Li is divisible into 14 independent processes. Each process 14 is formed of an ordered sub-list of the elementary tasks 10. The order of the elementary tasks 10 in each process 14 is the order of execution of the elementary tasks 10 in the initial list Li. Ii) the initial list Li is divisible into queues 18. Each queue 18 is associated with a resource 12. Each queue 18 is formed of an ordered sub-list of the elementary tasks 10 to be executed using the resource 12 with which it is associated. The order of the elementary tasks 10 in each sub-list 18 is the order of execution of the elementary tasks 10 in the initial list Li. Each queue 18 thus describes the utilization plan of the resource 12 to which it is associated. iii) the prerequisites for executing a given elementary task 10 are satisfied if and only if the prerequisites for executing the actions preceding said elementary task 10 in the process 14 and in the corresponding queue 18 are satisfied. The steps of the reordering process will now be described with reference to FIGS. 3, 4 and 5. An ordered list Lo of elementary tasks 10 to be executed is initially considered. It is assumed that a part of the elementary tasks 10 of the list Lo has been executed in the order of the list Lo. At an instant to, an unforeseen event interrupts the execution of the list Lo. The unforeseen event consists, for example, in modifying the duration d of an elementary task 10 not yet executed in the list Lo.

Alternatively, the list Lo is interrupted following the modification of the duration d of a basic task 10 running in the list Lo. In another variant, the list Lo is interrupted following the addition or removal, during the execution of the list, of a resource 12 or a process 14. As a variant again, the list Lo is interrupted more when an uncertainty arises as to the end of execution time Tf of an elementary task 10.

The initial list Li is formed of all the elementary tasks 10 of the list Lo remaining to be executed using the resources 12. The order of execution of the elementary tasks 10 of the initial list Li corresponds to the initial order execution of the list Lo, recalculated following the occurrence of the event. As illustrated in FIG. 3, the reordering method according to the invention advantageously comprises an initial compression step 19 of the initial list Li of elementary tasks 10. During the initial compression step 19, the initial list is applied to the initial list Li an algorithm known per se compression of the execution time Di of the initial list Li. The compression algorithm applied is for example an algorithm of the type PRF (Pednault Regnier and Fade) described for example in the document C. Backstrom , Computational aspects of reordering plans, JAIR vol. 99, 1998, pp. 99-137. During this initial step 19, the compression algorithm considers each elementary task 10, and delays or advances the start time of execution Ti of this elementary task so that the task is executed as soon as its prerequisites are met. execution are satisfied. From the initial list Li, the compression algorithm provides a secondary list Li 'of the elementary tasks 10. The order of execution of each elementary task 10 with respect to each elementary task 10 which conditions it is the same in the secondary list Li 'than in the initial list Li. The secondary list Li' has a duration of execution Di '. As known per se, the execution time Di 'corresponds to the maximum reduction of the execution time Di that can be obtained without modifying the order of execution of each elementary task 10 with respect to each elementary task which conditions it in the initial list In a next step 20, the elementary tasks 10 of the secondary list Li 'in independent processes 14 are grouped together. In other words, during this grouping step 20, the elementary tasks 10 of the initial list Li are grouped into independent processes 14. In a next step 24, the elementary tasks 10 of the secondary list Li 'are grouped into queues 18. During this grouping step 24, the elementary tasks 10 of the initial list Li are thus grouped into rows. In the exemplary embodiment, a first queue 18a is associated with the first resource 12a and includes the first elementary task 10a. A second queue 18b is associated with the second resource 12b. Alternatively, step 20 of grouping the elementary tasks in process and step 24 of grouping the elementary tasks into queues are performed simultaneously. During a next preselection step 28, a predetermined preselection algorithm is applied to the secondary list Li '. The steps of the pre-selection algorithm applied are illustrated in detail in FIG. 4. During a step 28a, an elementary modification is performed in the queues 18. The elementary modification considered must not lead to cycles. in the performance of the reordered elementary tasks, nor has it been previously defined as a prohibited modification. With respect to these conditions, the elementary modification consists, for example, in moving a target elementary task from a first queue associated with a first resource to a second queue associated with a second resource, of the same class as the first resource. Alternatively or additionally, the basic change is to move a target elementary task within its own queue. More particularly, the target elementary task is inserted in the second queue at a given position of the second queue. Then, if necessary, the instants of start of execution Ti and end of execution Tf of the elementary task following the target elementary task are delayed in the second queue. It also delays, if necessary, the times of start of execution Ti and end of execution Tf of the elementary task following the target elementary task in the process 14 comprising said target elementary task. In addition, if possible, the instants of start of execution Ti and end of execution Tf of the elementary task which followed the target elementary task in the first queue are advanced. Finally, if they have not been previously delayed, the instants of start of execution Ti and end of execution Tf of the elementary task following the target elementary task in the process 14 comprising said target elementary task are advanced. In the exemplary embodiment, the elementary modification consists for example in moving the first elementary task 10a of the first queue 18a to the first position of the second queue 18b associated with the resource 12b. During a next step 28b, a parameter p representative of the elementary modification performed during the preceding step 28a is calculated. For that purpose, fuzzy variables are built beforehand.

Each fuzzy variable is formed of a time interval representative of an uncertainty concerning the total execution time of a process 14. As a variant, each fuzzy variable is formed of a function of belonging to these time intervals, the notion of belonging being understood in the sense of fuzzy sets. The calculation of each fuzzy variable associated with a process 14 comprising a target elementary task notably involves: the elementary task following the target elementary task in the second queue, and / or the elementary task following the target elementary task in the second queue; the process 14 comprising said target elementary task, and / or - the elementary task that followed the target elementary task in the first queue. A first intermediate variable o and a second intermediate variable 62 are then calculated from the fuzzy variables constructed. The calculation of the first intermediate variable ai, respectively of the second intermediate variable a2 consists, for example, in determining the maximum value of the lower bounds, respectively of the upper bounds, of the fuzzy variables constructed. The value of the intermediate variables ai, 62 is provided by the result of each of these calculations. The representative parameter p is then calculated from the intermediate variables al, az, as well as from a risk aversion rate. The risk aversion rate is defined as the level of preference attributed to obtaining a guaranteed final list duration in relation to obtaining a potentially shorter, but unsecured, final list term. The representative parameter p is then, for example, expressed as follows: u = (1- a) .0-1 + ao-2 (1) At the end of step 28b, the parameter p representative of the elementary modification performed. During a next step 28c, it is tested whether all the elementary modifications possible, for all the elementary tasks 10 of all the queues 18, have been carried out. If the test is positive, a next step 28d is implemented. If the test is negative, step 28a is re-performed for another position of the target elementary task in a second queue, or for another target elementary task. During the following step 28d, at least one elementary modification is preselected satisfying a preselection criterion. The preselection criterion consists, for example, in comparing the value of each representative parameter p calculated in step 28b with the value of a threshold parameter ps. For a given elementary modification, if the value of the parameter p representative of this elementary modification is smaller than the value of the threshold parameter ps, the elementary modification is preselected. At the end of step 28d, the or each preselected elementary modification is stored in a memory. As a variant, the preselection criterion consists in preselecting the N1 elementary modifications whose associated representative parameter p has the lowest value, N1 being a previously fixed integer. Each of the N1 preselected elementary modifications is then stored in a memory.

During a next step 28e, for the or each elementary change preselected in the preceding step 28d, a modified list Lm of the elementary tasks 10 is determined. The or each modified list Lm of the elementary tasks 10 takes up the elementary tasks 10 of the secondary list Li 'in a different order. The new order of a modified list Lm given is the order as defined following the corresponding elementary modification. Each modified list Lm thus resumes the elementary tasks 10 of the initial list Li in a different order. At the end of step 28e, the or each modified list Lm is stored in a memory. During a subsequent step 28f, a datum representative of the or each modified list Lm stored in the preceding step 28e is determined. The determination of this representative data consists, for example, in calculating the execution time Dm of the or each modified list Lm. The representative data of a modified list Lm given is then the execution time Dm of this list. At the end of step 28f, the or each representative representative data item is stored in a memory. At the end of this same step 28f, a counter C is incremented. The counter C is representative of the number of elementary modifications carried out within a modified list Lm given. During a next step 28g, it is tested whether the value of the counter C is greater than or equal to a predefined number Nmax. Nmax is an integer representative of the maximum number of elementary changes within a given modified Lm list. If the test is positive, a next step is carried out. If the test is negative, step 28a is re-performed for the or each modified list Lm stored in step 28e. At the end of the steps 28a, 28b, 28c, 28d, 28e, 28f and 28g constituting step 28, several modified lists Lm satisfying the preselection criterion are thus preselected.

In the next step 30 shown in FIG. 3, the final list Lf reordered of the elementary tasks 10 from the set of modified lists Lm preselected during the preceding step 28 is selected, as detailed below. During this selection step, a predetermined selection algorithm is applied to the set of preselected modified Lm lists. The steps of the applied selection algorithm are illustrated in detail in FIG.

During a step 30a, at least one preselected modified list Lm is determined satisfying a first predetermined selection criterion. The first selection criterion consists in presenting the lowest representative data value among the set of modified lists Lm preselected. In the exemplary embodiment, the first selection criterion consists in presenting the lowest execution time value Dm among the set of modified lists Lm preselected. During a next step 30b, it is tested whether said at least one modified list Lm determined in the previous step 30a is unique. If the test is positive, the final list Lf reordered from the elementary tasks 10 is taken as identical to said modified list Lm, during a selection step 30c. If the test is negative, the modified lists Lm satisfying the first predetermined selection criterion are stored in a memory and a subsequent step 30d is implemented. In the following step 30d, from the modified lists Lm satisfying the first predetermined selection criterion, a modified list Lm satisfying a second predetermined selection criterion is determined. The second selection criterion consists, for example, of presenting the smallest distance O to the initial list Li. At the end of step 30d, the selection step 30c is carried out. During this selection step 30c, the final list Lf reordered from the elementary tasks 10 is taken as identical to the modified list Lm satisfying the second predetermined selection criterion. At the end of step 30, the elementary tasks 10 of the final list Lf reordered are executed during a final execution step, not shown in the figures. It is thus conceivable that the reordering method according to the invention makes it possible to limit the differences between the initial list and the final list, while ensuring a minimization of the duration of the final list. The reordering method according to the invention advantageously takes into account potential uncertainties on the execution time of at least one modified list, as well as potential uncertainties on the duration of the elementary tasks. It is advantageously independent of the modeling used for calculating the initial list of elementary tasks and is thus robust to possible errors due to the modeling used.

The reordering method according to the invention also has a lightened complexity compared to a reordering process of the prior art providing an optimal solution. It is suitable to be implemented several times during the execution of the elementary tasks of a current list. It is particularly suitable to be implemented whenever an unforeseen event of the aforementioned type interrupts the execution of the current list. The choice of the values of the threshold parameter ps, and the integers N1 and Nmax advantageously makes it possible to improve the performance and the speed of execution of the reordering method according to the invention. For example, N1 is advantageously equal to 10. In this case, the threshold parameter ps is adjusted to preselect only 10 elementary modifications. Nmax is advantageously between 3 and the maximum number of elementary tasks 10 that can be found in a process 14 of the initial list Li.

The description has been made in particular with reference to a reordering process of a management plan of a crisis situation. It is understood, however, that the invention applies in the same way to any initial ordered list of elementary tasks satisfying the aforementioned hypotheses. The present invention also relates to a computer program product comprising the software instructions which, when implemented by a processing unit, implement the steps of the reordering method as defined in the present description, relatively an ordered initial list of basic tasks to be performed using resources. Another subject of the present invention is a computer comprising a processing unit able to implement the steps of the reordering method as defined in the present description, with respect to an initial ordered list of elementary tasks to be executed using resources. .

Claims (10)

CLAIMS.-A computer-implemented method of reordering an ordered initial list (Li) of elementary tasks (10) to be executed using resources (12) into a reordered final list (Lf) of elementary tasks (10), the resources (12) being non-shareable and being grouped into classes (16) of resources (12), each elementary task (10) being executable by each resource (12) of the same class (16) , each elementary task (10) being associated in the initial list (Li) with a resource (12), characterized in that it comprises the following steps: - the grouping (20) of the elementary tasks (10) of the initial list (Li) in process (14), each process (14) being formed of an ordered sub-list of elementary tasks (10), each elementary task (10) belonging to a process (14), the processes (14) being independent - grouping (24) elementary tasks (10) into queues te (18), each queue (18) being associated with a respective resource (12) and formed of an ordered sub-list of elementary tasks (10) to be executed using this resource (12), preselection (28) of a plurality of modified lists (Lm) of elementary tasks (10) satisfying a predetermined pre-selection criterion, by applying a first predetermined algorithm to the initial list (Li), each modified list (Lm); ) taking up the elementary tasks (10) of the initial list (Li) in a different order, and - selecting (30) the final list (Lf) from among the modified lists (Lm) by applying a second predetermined algorithm to the set of modified lists (Lm). 2. The method of claim 1, wherein the first algorithm comprises: the realization (28a) of an elementary modification consisting in moving a target elementary task (10) of a first queue of a first resource to a second queue of a second resource of the same class as the first resource, - the calculation (28b) of a parameter (p) representative of the elementary modification, said representative parameter (p) being calculated from a time interval representative of an uncertainty concerning the duration of execution, following said elementary modification, of at least one process (14), - the iteration (28c) of the two preceding steps step by step, for each elementary task (10) of each queue (18), and for each position of the elementary task in a second queue, - preselection (28d), according to the preselection criterion, of at least one modification ed elementary, - the determination (28e) of a modified list (Lm) respectively for the or each preselected elementary modification, - the determination (28f) of a datum (Dm) representative of the or each modified list (Lm), - the iteration (28g) of the six preceding steps from each modified list (Lm) determined at the previous iteration, until reaching a predefined maximum number (Nmax) of elementary modifications within a modified list (Lm) compared to the initial list (Li). 3. A method according to claim 2, wherein the step (28f) of determining a datum (Dm) representative of the or each modified list (Lm) consists in calculating the duration (Dm) of execution of this list. modified (Lm), the representative datum (Dm) being the result of this calculation. 4. A method according to claim 2 or 3, wherein the step (28b) of calculating a parameter (p) representative of the elementary modification comprises the prior construction of fuzzy variables, each fuzzy variable being formed of an interval temporal representative of an uncertainty concerning the duration of execution, following said elementary modification, of a complex task (14), the representative parameter (p) being calculated from the fuzzy variables constructed. 5.- Method according to one of claims 2 to 4, wherein during step (28b) of calculating a parameter representative of the elementary modification, the representative parameter (p) is calculated from a rate (a) risk aversion, the risk aversion rate (a) being the level of preference attributed to obtaining a guaranteed final list duration (Lf) in relation to obtaining a duration of the final list (Lf) potentially shorter, but not guaranteed. 6. A method according to any one of the preceding claims, wherein during step (30) for selecting the final list (Lf), the second algorithm comprises a step (30a) for determining at least one list. preselected (Lm) satisfying a first predetermined selection criterion, and a step (30c) for selecting the final list (Lf) from among the at least one preselected list (Lm). 7. The method of claim 6, wherein the second algorithm further comprises a step (30b) for testing the uniqueness of said at least one preselected list (Lm), the final list (Lf) being taken as identical to said preselected list (Lm) during the step (30c) of selecting the final list (Lf), if the uniqueness test is positive. The method of claim 7, further comprising, if the uniqueness test is negative in the test step (30b), a determining step (30d) of the plurality of preselected lists (Lm) satisfying the first predetermined selection criterion, of a preselected list (Lm) satisfying a second predetermined selection criterion, the final list (Lf) being taken as identical to the said preselected list (Lm) during the selection step (30c) of the final list (Lf). 9. A method according to claim 8, wherein during step (30d) of determining a preselected list (Lm) satisfying a second predetermined selection criterion, the second predetermined selection criterion is to present the smallest distance. (0) to the initial list (Li), the distance (D) from a first list to a second list being the square root of the sum of the squares of the time differences between the start times of execution Ti) (d) on the one hand, and time differences between the times of completion (Tf) on the other hand, between the elementary tasks (10) of the first and second lists which belong to the same process (14) and are associated with resources (12) different from the same class (16) of resources (12). 10. A method according to any one of the preceding claims, comprising an initial step (19) of compressing the initial list (Li) of elementary tasks (10), the compression consisting in the maximum reduction of the duration (Dm) of executing said initial list (Li) that can be obtained without modifying the order of execution of each elementary task (10) with respect to each elementary task (10) which conditions it in this list (Li).